Consider the circuit shown in Figure P1.68. Find the current i_R flowing through the resistor. Find the power for each element in the circuit. Which elements are absorbing energy?
Here is a picture of 1.68
The Attempt at a Solution
So what I did first was I set up two KVL loops, one in the left side which consists of of both the Voltage Source and the Current Source and the other in the right side of the loop.
1.) 4(R_current source) - 12V = 0V
2.) 12V + R( i_R) = 0V
Solving the second equation I see get that i_R= -1.5A
Then using passive sign convention I get that P_resistor= ((-1.5)^2)*8= 18 => the resistor is drawing 18 Watts.
Solving the first loop it is apparent that no matter what the resistance is in the current source the outcome of V=IR is going to be 12.
To get the current through the voltage source I did a KCL at the node above the voltage source. Doing this I got that I_current source = I_voltage + i_R
with i_R going in the direction indicated in Figure 1.68 and I_voltage going from the negative terminal to the positive terminal of the voltage source.
which is turns into 8= I_voltage - 1.5 => I_voltage= 9.5 A
P_Voltage= -(9.5)(12V)= -114 W
And P_current= (8)(12V)= - 96 W
As you can see the power of the circuit does not equal zero and thus I am doing something very very wrong.